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Dynamic analysis of time fractional order phytoplankton–toxic phytoplankton–zooplankton system

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  • Javidi, Mohammad
  • Ahmad, Bashir

Abstract

In this paper, we study the dynamics of a time fractional order toxic-phytoplankton–phytoplankton–zooplankton system (TPPZS). Routh–Hurwitz criteria is applied to discuss the stability analysis of biologically feasible equilibrium points for the given system in terms of reproduction numbers (associated with ecological as well as disease phenomena). Local stability properties of the toxic-phytoplankton-free equilibrium are also investigated. Numerical simulations are performed for a hypothetical set of parameter values in support of our analytic results.

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  • Javidi, Mohammad & Ahmad, Bashir, 2015. "Dynamic analysis of time fractional order phytoplankton–toxic phytoplankton–zooplankton system," Ecological Modelling, Elsevier, vol. 318(C), pages 8-18.
    • Handle: RePEc:eee:ecomod:v:318:y:2015:i:c:p:8-18
    DOI: 10.1016/j.ecolmodel.2015.06.016
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    12. Fatmawati, & Khan, Muhammad Altaf & Azizah, Muftiyatul & Windarto, & Ullah, Saif, 2019. "A fractional model for the dynamics of competition between commercial and rural banks in Indonesia," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 32-46.
    13. Bashir Ahmad & Madeaha Alghanmi & Ahmed Alsaedi & Hari M. Srivastava & Sotiris K. Ntouyas, 2019. "The Langevin Equation in Terms of Generalized Liouville–Caputo Derivatives with Nonlocal Boundary Conditions Involving a Generalized Fractional Integral," Mathematics, MDPI, vol. 7(6), pages 1-10, June.
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